我想知道如何计算两个椭圆之间的交点,例如如图所示该图中云芝和virginca之间的交点的体积: ,其使用基于此tutorial以下兆瓦绘制:如何计算r中椭圆交点的体积
data(iris)
log.ir <- log(iris[, 1:4])
ir.species <- iris[, 5]
ir.pca <- prcomp(log.ir, center = TRUE, scale. = TRUE)
library(ggbiplot)
g <- ggbiplot(ir.pca, obs.scale = 1, var.scale = 1,
groups = ir.species, ellipse = TRUE,
circle = TRUE)
g <- g + scale_color_discrete(name = '')
g <- g + theme(legend.direction = 'horizontal',
legend.position = 'top')
print(g)
我得到为椭圆的协方差和中心如下:
setosa.cov <- cov(ir.pca$x[ir.species=="setosa",])
versicolor.cov <- cov(ir.pca$x[ir.species=="versicolor",])
virginica.cov <- cov(ir.pca$x[ir.species=="virginica",])
setosa.centre <- colMeans(ir.pca$x[ir.species=="setosa",])
versicolor.centre <- colMeans(ir.pca$x[ir.species=="versicolor",])
virginica.centre <- colMeans(ir.pca$x[ir.species=="virginica",])
但是,然后我在我的智慧结束: - |
编辑: 继@下面卡尔witthoft,这里的例子使用SIAR ::重叠的适应症:
library(siar)
setosa <- ir.pca$x[ir.species=="setosa",]
versicolor <- ir.pca$x[ir.species=="versicolor",]
virginica <- ir.pca$x[ir.species=="virginica",]
overlap.fun <- function(data.1, data.2){
dimensions <- ncol(data.1)
for(i in 1:(dimensions-1)){
overlap.out <- overlap(data.1[,i], data.1[,i+1], data.2[,i], data.2[,i+1], steps = 5)
out$overlap[i] <- overlap.out$overlap
out$area1[i] <- overlap.out$area1
out$area2[i] <- overlap.out$area2
}
return(out)
}
overlap.fun(versicolor, virginica)
回报:
$overlap
[1] 0.01587977 0.48477088 0.08375927
$area1
[1]1.020596 1.04614461 0.08758691
$area2
[1] 1.028594 1.1535106 0.1208483
奇怪的是当我做了百分比计算的值并不真正对应于ggbiplot PCA中的椭球:
tmp <- overlap(versicolor[,1], versicolor[,2], virginica[,1], virginica[,2], steps = 5)
virginica.percentage <- round(x=(tmp$overlap/tmp$area2*100), digits = 2)
versicolor.percentage <- round(x=(tmp$overlap/tmp$area1*100), digits = 2)
> virginica.percentage [1] 1.54
> versicolor.percentage[1] 1.56
这比上面的图1中所示的要小得多。 但是可能更好的在这个here上打开另一个线程。
基本的方法是找到相交点,计算“上”和“下”曲线的积分,并取距离,您需要将其分开以确保每个积分超过单值d功能范围。也就是说,我似乎记得在CRAN上有一两个包含这种相交面积计算的软件包。当然我不记得哪些:-( –